Chapter 19, Problem 6AR

To determine

(a)

To evaluate the given expression.

Answer to Problem 6AR

  $\frac{3}{4}$

Explanation of Solution

Given information:

An expression is given as $\frac{1}{8}+\frac{5}{8}$

Calculation:

We have been given an expression as $\frac{1}{8}+\frac{5}{8}$.

Evaluating the expression,

  $\begin{array}{l}\frac{1}{8}+\frac{5}{8}=\frac{1+5}{8}\\ =\frac{6}{8}=\frac{\cancel{2}\times 3}{\cancel{2}\times 4}\\ =\frac{3}{4}\end{array}$

Hence, $\frac{1}{8}+\frac{5}{8}$$=$$\frac{3}{4}$.

To determine

(b)

To add the given fractions.

Answer to Problem 6AR

  $\frac{11}{8}$

Explanation of Solution

Given information:

An expression is given as $\frac{7}{16}+\frac{15}{16}$

Calculation:

We have been given an expression as $\frac{7}{16}+\frac{15}{16}$.

Evaluating the expression,

  $\begin{array}{l}\frac{7}{16}+\frac{15}{16}=\frac{7+15}{16}\\ =\frac{22}{16}=\frac{\cancel{2}\times 11}{\cancel{2}\times 8}\\ =\frac{11}{8}\end{array}$

Hence, $\frac{7}{16}+\frac{15}{16}$$=$$\frac{11}{8}$.

To determine

(c)

To evaluate the given expression.

Answer to Problem 6AR

  $\frac{33}{32}$

Explanation of Solution

Given information:

An expression is given as $\frac{5}{8}+\frac{13}{32}$

Calculation:

We have been given an expression as $\frac{5}{8}+\frac{13}{32}$.

Evaluating the expression,

  $\begin{array}{l}\frac{5}{8}+\frac{13}{32}=\frac{5}{8}\times \frac{4}{4}+\frac{13}{32}\\ =\frac{20}{32}+\frac{13}{32}=\frac{20+13}{32}\\ =\frac{33}{32}\end{array}$

Hence, $\frac{5}{8}+\frac{13}{32}$$=$$\frac{33}{32}$.

To determine

(d)

To find the simplified value of given fractions.

Answer to Problem 6AR

  $\frac{419}{100}$

Explanation of Solution

Given information:

An expression is given as $3\frac{7}{10}+\frac{49}{100}$

Calculation:

We have been given an expression as $3\frac{7}{10}+\frac{49}{100}$.

Evaluating the expression,

  $\begin{array}{l}3\frac{7}{10}+\frac{49}{100}=\frac{3\times 10+7}{10}+\frac{49}{100}\\ =\frac{37}{10}+\frac{49}{100}=\frac{37}{10}\times \frac{10}{10}+\frac{49}{100}\\ =\frac{370}{100}+\frac{49}{100}=\frac{370+49}{100}\\ =\frac{419}{100}\end{array}$

Hence, $3\frac{7}{10}+\frac{49}{100}$$=$$\frac{419}{100}$.

To determine

(e)

To evaluate the given expression.

Answer to Problem 6AR

  $\frac{55}{64}$

Explanation of Solution

Given information:

An expression is given as $\frac{9}{32}+\frac{1}{4}+\frac{21}{64}$

Calculation:

We have been given an expression as $\frac{9}{32}+\frac{1}{4}+\frac{21}{64}$.

Evaluating the expression,

  $\begin{array}{l}\frac{9}{32}+\frac{1}{4}+\frac{21}{64}=\frac{9}{32}\times \frac{2}{2}+\frac{1}{4}\times \frac{16}{16}+\frac{21}{64}\\ =\frac{18}{64}+\frac{16}{64}+\frac{21}{64}=\frac{18+16+21}{64}\\ =\frac{55}{64}\end{array}$

Hence, $\frac{9}{32}+\frac{1}{4}+\frac{21}{64}$$=$$\frac{55}{64}$.

To determine

(f)

To subtract the given fractions.

Answer to Problem 6AR

  $\frac{1}{4}$

Explanation of Solution

Given information:

An expression is given as $\frac{11}{16}-\frac{7}{16}$

Calculation:

We have been given an expression as $\frac{11}{16}-\frac{7}{16}$.

Evaluating the expression,

  $\begin{array}{l}\frac{11}{16}-\frac{7}{16}=\frac{11-7}{16}\\ =\frac{4}{16}=\frac{\cancel{4}}{\cancel{4}\times 4}\\ =\frac{1}{4}\end{array}$

Hence, $\frac{11}{16}-\frac{7}{16}$$=$$\frac{1}{4}$.

To determine

(g)

To subtract the given fractions.

Answer to Problem 6AR

  $\frac{1}{4}$

Explanation of Solution

Given information:

An expression is given as $\frac{17}{20}-\frac{3}{5}$

Calculation:

We have been given an expression as $\frac{17}{20}-\frac{3}{5}$.

Evaluating the expression,

  $\begin{array}{l}\frac{17}{20}-\frac{3}{5}=\frac{17}{20}-\frac{3}{5}\times \frac{4}{4}\\ =\frac{17}{20}-\frac{12}{20}=\frac{5}{20}\\ =\frac{\cancel{5}}{\cancel{5}\times 4}\\ =\frac{1}{4}\end{array}$

Hence, $\frac{17}{20}-\frac{3}{5}$$=$$\frac{1}{4}$.

To determine

(h)

To find the simplified value of given fractions.

Answer to Problem 6AR

  $\frac{25}{16}$

Explanation of Solution

Given information:

An expression is given as $\frac{49}{64}-\frac{3}{8}$

Calculation:

We have been given an expression as $\frac{49}{64}-\frac{3}{8}$.

Evaluating the expression,

  $\begin{array}{l}\frac{49}{64}-\frac{3}{8}=\frac{49}{64}-\frac{3}{8}\times \frac{8}{8}\\ =\frac{49}{64}-\frac{24}{64}=\frac{49-24}{64}\\ =\frac{25}{64}\end{array}$

Hence, $\frac{49}{64}-\frac{3}{8}$$=$$\frac{25}{16}$.

To determine

(i)

To find the simplified value of given fractions.

Answer to Problem 6AR

  $\frac{85}{16}$

Explanation of Solution

Given information:

An expression is given as $6-\frac{11}{16}$

Calculation:

We have been given an expression as $6-\frac{11}{16}$.

Evaluating the expression,

  $\begin{array}{l}6-\frac{11}{16}=\frac{6\times 16}{16}-\frac{11}{16}\\ =\frac{96}{16}-\frac{11}{16}=\frac{96-11}{16}\\ =\frac{85}{16}\end{array}$

Hence, $6-\frac{11}{16}$$=$$\frac{85}{16}$.

To determine

(j)

To find the simplified value of given fractions.

Answer to Problem 6AR

  $\frac{125}{32}$

Explanation of Solution

Given information:

An expression is given as $13\frac{1}{8}-9\frac{7}{32}$

Calculation:

We have been given an expression as $13\frac{1}{8}-9\frac{7}{32}$.

Evaluating the expression,

  $\begin{array}{l}13\frac{1}{8}-9\frac{7}{32}=\frac{13\times 8+1}{8}-\frac{9\times 32+7}{32}\\ =\frac{105}{8}-\frac{295}{32}=\frac{105}{8}\times \frac{4}{4}-\frac{295}{32}\\ =\frac{420-295}{32}\\ =\frac{125}{32}\end{array}$

Hence, $13\frac{1}{8}-9\frac{7}{32}$$=$$\frac{125}{32}$.